The 24-year-old will link up with fellow England internationals Chris Smalling and Tammy Abraham under Jose Mourinho at the Serie A club.
Maitland-Niles has made eight appearances for Arsenal this season but has not featured since coming off the bench in the 4-0 defeat at Liverpool in November.
Mourinho has reportedly been seeking reinforcements at full-back, with Italy international Leonardo Spinazzola missing since suffering an Achilles injury at UEFA Euro 2020.
Maitland-Niles, who can play at full-back or in midfield, spent the second half of last season on loan at West Bromwich Albion, where he made 15 appearances for the ultimately relegated Baggies.
The player appeared to try and force a move away from the Gunners in August when he took to Instagram to say: "All I want to do is go where I'm wanted and where I'm going to play."
However, a reported move to Everton failed to materialise and Maitland-Niles eventually agreed to stay at the north London club until January.